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A). Appendix C gives a detailed mathematical description of the relationship between accumulator contents and the PD output waveform. It is also possible to drive a phase or delay modulator, at the frequency divider output, with the same compensation signal, thus canceling the phase modulation rather than the resulting voltage [Banerjee, 2008]. If the modulator is placed at the frequency divider input, the required phase modulation does not depend on N, but time delay modulation would. We will not consider cancellation by phase modulation further.

Advantages of fractional-N synthesis include - reduced step size while maintaining wide loop bandwidth, and - reduced noise at the output because of the smaller divide ratio. Accumulators are used to convert the fractional divide number into an equivalent series of whole numbers. A simple fractional-N synthesizer needs a narrow bandwidth to filter the PD waveform caused by the sequencing of N-values. The bandwidth can be widened if the PD waveform is canceled by a signal derived from the accumulators.

The former provides a smooth noise plot at the level shown in Fig. 625 MHz, q ¼ 1. Noise bandwidth Bn ¼ 3750 Hz in (a) and 117 Hz in (b). 625 MHz, q ¼ 2. Noise bandwidth Bn ¼ 3750 Hz in (a) and 117 Hz in (b). by H(Df), but the latter does not. Pamarti and Galton [2007] have found that in order for the dither to be effective in eliminating spurs, q pÀ2; ð3:2Þ which implies that the q ¼ 2 curve in Fig. 2 should not be used with the p ¼ 3 MASH. We could increase the order of the modulator to p ¼ 4 and see the spectrum become smooth again.